BGE. Is it possible to create transparent plane with blur filter?
I never used BGE and you blend file link gives a 403, but here's how I'd implement that effect:

Normally in a game engine:

Render your scene to a texture. That's the first step you normally do for post-processing.

Render the glass pane to another texture. The glass pane should be white, the rest black. Disable material and light for faster rendering. If your glass pane is partially hidden by other objects, these parts should also be black in your rendering.

Blur your original rendering. Use the black/white texture as a mask so only the glass pane gets blurred. Alternatively, blur the whole image in a copy and use the texture to combine both.

In Blender:

Here's my node setup with an exaggerated version of the effect. On the right, the blur map. I used the object ID pass to generate it.